|
The information encoded in initial ideals
Author(s):
Gunnar
Fløystad;
Mark
L.
Green
Journal:
Trans. Amer. Math. Soc.
353
(2001),
1427-1453.
MSC (2000):
Primary 13P10;
Secondary 14H50
Posted:
November 29, 2000
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We consider homogeneous ideals  and the initial ideal  for the revlex order. First we give a sequence of invariants computed from  giving better and better ``approximations" to the initial ideal and ending in an equivalent description. Then we apply this to different settings in algebraic geometry to understand what information is encoded in the generic initial ideal of the ideal of a projective scheme. We also consider the higher initial ideals as defined in a paper by Fløystad. In particular, we show that giving the generic higher initial ideal of a space curve is equivalent to giving the generic initial ideal of a linked curve.
References:
-
- 1.
- D. Bayer, M. Stillman. A criterion for detecting m-regularity. Inventiones Matematicae 87 (1987), 1-11. MR 87k:13019
- 2.
- C. v. Bothmer. Thesis, University of Bayreuth (1995).
- 3.
- M. Cook. The connectedness of space curve invariants. Compositio Mathematica 111 no.2 (1998). MR 99a:14040
- 4.
- D. Eisenbud. Commutative algebra with a view towards algebraic geometry. Springer-Verlag, 1995. MR 97a:13001
- 5.
- G. Fløystad. Higher initial ideals of homogeneous ideals. Memoirs of the American Mathematical Society 134 no. 638 (1998). MR 98m:13021
- 6.
- G. Fløystad. A property deducible from the generic initial ideal. Journal of Pure and Applied Algebra 136 (1999), 127-140. MR 2000c:13039
- 7.
- A. Galligo. A propos du theoreme de preparation de Weierstrass. Fonctions de Plusieurs Variables Complexes (Sém. François Norquet, 1970-1972), Lecture Notes in Mathematics, vol. 409, Springer-Verlag, 1973, pp. 543-579. MR 53:5924
- 8.
- M. Green. Generic initial ideals. Summer school on commutative algebra, Barcelona 16. - 26. July 1996. Accompanying notes, volume II.
- 9.
- L. Gruson, C. Peskine. Genre des courbes de l'espace projectif, Algebraic Geometry: Proc. Symposium University of Tromsø, 1977, Lecture Notes in Mathematics, vol. 687, Springer-Verlag, 1978, pp. 31-59. MR 81e:14019
- 10.
- R. Liebling. Classification of space curves using initial ideals. Ph.D. thesis, University of California at Berkeley, (1996).
- 11.
- M. Martin-Deschamps, D. Perrin. Sur la classification des courbes gauches. Astérisque 184-185 (1990). MR 91h:14039
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
13P10,
14H50
Retrieve articles in all Journals with MSC
(2000):
13P10,
14H50
Additional Information:
Gunnar
Fløystad
Affiliation:
Matematisk Institutt, Johs. Brunsgate 12, 5008 Bergen, Norway
Email:
gunnar@mi.uib.no
Mark
L.
Green
Affiliation:
Department of Mathematics, University of California at Los Angeles, Los Angeles, California 90024
Email:
mlg@math.ucla.edu
DOI:
10.1090/S0002-9947-00-02737-9
PII:
S 0002-9947(00)02737-9
Received by editor(s):
June 5, 1999
Posted:
November 29, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org